Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×Dic262 | C2 | semidirect |
| 3. #22553659 | C2 | semidirect |
| 4. #22553657 | C2 | semidirect |
| 5. #22553602 | C2 | semidirect |
| 6. #22553601 | C2 | semidirect |
| 7. #22553512 | C2 | semidirect |
| 8. #22553510 | C2 | semidirect |
| 9. C8×Dic262 | C2 | semidirect |
| 10. #22553397 | C2 | semidirect |
| 11. C4×SD16×C131 | C2 | semidirect |
| 77. Dic262 | SD16 | semidirect |
| 91. Q8×C131 | #41 | semidirect |
| 125. C131 | #3362 | semidirect |
| 137. C4×SD16 | D131 | semidirect |
| 206. Q8 | #14523513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic262 | 2 |
| #22553983 | 2 |
| #22553659 | 2 |
| #22553657 | 2 |
| #22553602 | 2 |
| #22553601 | 2 |
| #22553512 | 2 |
| #22553510 | 2 |
| C8×Dic262 | 2 |
| #22553397 | 2 |
| C4×SD16×C131 | 2 |
| #3362 | 131 |